x>0,y>0,且x y>2,求证1 x y,1 y 2中至少有一个小于2
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3x^2-2xy-8y^2=0,(3x+4y)(x-2y)=03x+4y=0,或,x-2y=03x=-4y,或,x=2yx/y=-4/3,或,x/y=2
x-3y=0x=3yx*2-xy+y*2/x*2+xy+y*2=(9y^2-3y^2+y^2)/(9y^2+3y^2+y^2)=7y^2/13y^2=7/13
3x²-2xy-8y²=0两边同除y²得:3(x/y)²-2(x/y)-8=0(3x/y+4)(x/y-2)=0x/y=2或x/y=-4/3
把他拆成x平方+1/2xy+1/2xy然后利用基本不等式,接下来你应该会做的,我打起来太麻烦
因为xy不为0,所以3x^2-2xy-8y^2=0可以两边同时除以y^2,得3(x/y)^2-2(x/y)-8=0即(3x/y+4)(x/y-2)=0解得x/y=2或者x/y=-4/3希望有用.
x-5xy+6y=0(√x-2√y)(√x-3√y)=0所以√x=2√y,√x=3√yx=4y或x=9y原式=(8y)/(9y)=8/9或=(14y)/(20y)=7/10
3x²-2xy-8y²=0(x-2y)(3x+4y)=0x=2y或3x=-4yx/y=2或x/y=-4/3
xy≠0,所以x≠0,y≠03x²-2xy-8y²=0两边除于xy3(x/y)-2-8(y/x)=0设x/y=t;t≠03t-8/t-2=03t²-2t-8=0(t-2)
题目不很清楚哈,我理解是:已知:x-(xy)^0.5-2y=0;求:(2x-(xy)^0.5)/(y+2*(xy)^0.5);由已知:(x/y)-(x/y)^0.5-2=0;[(X/y)^0.5-2]
是不是x-5√xy-6y=0?(√x-6√y)(√x+√y)=0x>0,y>0则√x+√y>0所以√x-6√y=0√x=6√yx=36y所以√xy=6y所以原式=(36y-12y+y)/(36y+6y
由x-√xy-2y=0可知,(√x+√y)(√x-2√y)=0解得√x=2√y,即x=4y则(2x-√xy)/(y+2√xy)=(2x-2y)/(y+4y)=6/5
3x²-2xy-8y²=0(3x+4y)(x-2y)=03x=-4y,x=2y所以x/y=-4/3或2
x-√(xy)-2y=(√x-2√y)(√x+√y)=0因为x>0,y>0所以√x+√y>0所以√x=2√yx=4y2x=8y,√(xy)=2√y*√y=2y原式=(8y-2y)÷(y+4y)=6y/
2x+3y=8=>x=(8-3y)/2xy=(8-3y)/2*y=1/2*(-3y^2+8y)=-3/2*(y^2-8/3y+16/9)+8/3=-3/2(y-4/3)^2+3/8《8/3所以最大值为
因为x>0,y>0,所以将x-根号xy-2y=0因式分解得(根号x-2根号y)(根号x+根号y)=0所以根号x=2根号y,即x=4y后面请自己代入吧,我看不懂你的表述.不好意思了
x^2-7xy+12y=0,且x.y不等于0(x-3y)(x-4y)=0x=3y或x=4y(x^2-2xy+y^2)/(2xy)=(x-y)^2/(2xy)x=3y时原式=4y^2/(6y^2)=2/
2X^2+3xy-2y^2=0(2x-y)(x+2y)=0即:2x-y=0或,x+2y=0y=2x或x=-2y当y=2x时:x+y/x-y=3x/(-x)=-3当x=-2y时:x+y/x-y=-y/(
∵x-y=4xy∴原式=[2(x-y)+3xy]/[-(x-y)-2xy]=(8xy+3xy)/(-4xy-2xy)=11xy/(-6xy)=-11/6